Something I noticed in Jedi:Luke tells the Emperor "Your overconfidence is your weakness." to which the Emperor replies "Your faith in your friends is yours".But actually....wasn't the reverse true in both cases?

Luke was so overconfident,he didn't even seem to allow for the possibility that Vader would in fact turn him over to the Emperor.Needless to say,throwing away his lightsaber in front of the Emperor was also overconfident.

Palpatine's faith in Vader (whom he calls "My friend") was fairly extreme,since he thought he could torture his son to death right in front of him without Vader batting an eye.One could make the case his faith in his Empire could fall in that category .

Interesting assertion, never thought about it that way before.

I don't think Luke throwing away his lightsaber was overconfidence as much as not allowing himself any further temptation to give into violence. Since he's never encountered any Sith Lords before, and Yoda obviously never got around to that "absorb the lightning in the palm of your hand" maneuver, he didn't know the Emperor wasn't exactly what he appeared to be: a frail old man surrounded by guards.